I don’t know what it would cost to enter local markets only, but I suspect that has less utility than being national or international. I don’t want a taxi app per city, I want the same app to get me to/from LAX to get me to/from JFK, and I doubt that’s my particular quirk.
On the latter, I don’t know what would happen if they charged monopoly prices. I suspect you’re right, cabs might come back.